Size-Dependent Persistent Luminescence of YAGG:Cr3+ Nanophosphors

In the current work, YAGG:Cr3+ nanophosphors were synthesized by the Pechini method and then annealed at different temperatures in the range 800–1300 °C. The structure and morphology of the samples were characterized by X-ray Powder Diffraction (XRPD). The lattice parameters and average crystalline sizes as site occupation by Al3+ and Ga3+ ions were calculated from the Rietveld refinement data. To investigate the effect of crystalline size of the materials on their optical properties: excitation and emission spectra were recorded and analyzed. Finally, the effect of crystalline size on the probability of carrier recombination leading to PersL was determined experimentally with thermoluminescence analyses. The Tmax-Tstop method was applied to determine the trap type and particle size (calcination temperature) effect on their redistribution. A correlation between structural changes and trap redistribution was found. In particular, the extinction of high-temperature TL maximum with increasing annealing temperatures is observed, while low-temperature TL maximum increases and reaches a maximum when the lattice parameter reaches saturation.


Introduction
The recently observed increase in interest in nanomaterials that could combine luminescent properties with the ability of temporary storage and emission release due to thermal (thermoluminescence, TL) and optical (optically stimulated luminescence, OSL) stimuli has resulted in the numerous publications on so-called persistent nanophosphors [1][2][3][4][5][6][7]. Due to potential biomedical applications, the most studied compounds are chemically stable oxides with spinel and garnet structures that provide better biocompatibility compared to, for example, fluorides and sulfides. In these materials, specific positions in the crystal lattice are defined, which can be substituted in a controlled way with acceptor and donor ions involved in the mechanism of electron and hole trapping, as well as their release leading to radiative deactivation [2,8]. An additional advantage of garnet and spinel structured materials is the ability to simultaneously control the energy gap value of the host material by introducing appropriate concentrations of other cations [9].
Ceramics and micro and nanocrystals based on the garnet matrix are the most perspective oxide crystals widely used as the active medium in solid-state lasers. Due to the anisotropic optical properties, YAG powders doped with rare-earth (Ce 3+ , Pr 3+ , Yb 3+ , and Nd 3+ ) and transition metals (Mn 2+ , Cr 3+ , etc.) are suitable for preparing transparent laser ceramics with the working region in the near-infrared range that is suitable for bio-applications [10]. At the same time, several publications have described the modulation of the band gap by replacing Ga 3+ with Al 3+ in the Y 3 Al 5-x Ga x O 12 matrix to obtain Y 3 Al 2 Ga 3 O 12 (YAGG) stoichiometry, which has been shown to be optimal for use as garnet PersL host material [9,11,12]. As a result, YAGG:Cr co-doped with lanthanides have gained attention due to their interesting persistent luminescence (PersL) in the visible, red, and NIR range, where Cr ions play an important role in obtaining long-lasting emissions.
Unfortunately, the theoretically very predictable results of the above actions for optimizing persistent luminescence (PersL) quality (intensity and duration) are perturbed in nanoscale particles due to structural imperfections related to size effects as well as the greater influence of the environment of these particles on radiative and non-radiative processes occurring in their volume [13]. Additionally, garnet powder is a convenient material for the manufacture of laser and persistent luminescence ceramics from nanosized grains by low-temperature sintering under high pressure [14,15]. Furthermore, the duration and color of PersL are determined by the luminescence center. Therefore, the use of Cr ions both as an independent dopant and as a co-dopant extends the emission time for most of the used matrices and shifts the emission range to the NIR region [9,[16][17][18].
In this work, we present the results of a spectroscopic study that allow us to better understand the influence of these effects using a model system of Y 3 Al 2 Ga 3 O 12 garnet (YAGG) doped only with chromium ions, which, according to previously accepted models, act both as dopants leading to the formation of trapping centers and leading to the production of PersL. The presented here results of a detailed analysis of traps based on the T max -T stop method in correlation with structural changes-particularly site occupancy-will, in our opinion, help to establish the relationship between structural changes in crystals and their effect on traps creation and redistribution.

Characterization Techniques
X-ray powder diffraction (XRPD) patterns were acquired by a PANalytical X'Pert pro X-ray (Malvern Pananalytical, Malvern, UK) powder diffractometer at 40 kV and 30 mA in the 2θ range of 10-80 • (2θ step: 0.02626 • ) using nickel-filtered Cu K α1 radiation. The phase identification was performed using the X'pert HighScore Software. The phase composition, cell parameters, crystallite sizes, and microstrain as the occupancy of the octahedral and tetrahedral sites in the YAGG structures were evaluated based on the Rietveld method [20] using the WinPLOTR, and WinPLOTR-2006 applications. The average crystallite size was calculated using a Williamson-Hall analysis.
Photoluminescence emission (PL) and excitation (PLE) spectra were measured using the FLS980 Fluorescence Spectrometer (Edinburgh Instruments Ltd., Livingston, UK) equipped with a 450 W Xenon lamp as an excitation source. The excitation arm was supplied with a holographic grating of 1800 lines/mm, blazed at 300 nm, while the emission arm was supplied with ruled grating, 1800 lines/mm blazed at 750 nm. Both the excitation and emission monochromators were in the Czerny-Turner configuration. The photomultiplier tube R928P (Hamamatsu Photonics, Shizuoka, Japan) was used as a detector. The scanning range was from 250 to 680 nm for the PLE spectrum and from 460 to 820 nm for the PL spectrum with a spectral resolution of 0.2 nm. All spectra were corrected for the sensitivity of detectors and intensity excitation source.
The thermoluminescence (TL) glow curves were collected with a lexygresearch-Fully Automated TL/OSL Reader (Freiberg Instruments GmbH, Freiberg, Germany) from room temperature to 300 • C with heating rates 2, 1, 0.75, 0.5, and 0.25 • C·s −1 . Varian VF-50J/S RTG tube (Varian Medical Systems Inc., Palo Alto, CA, USA) with tungsten core and copper case as an X-ray radiation source was used as an irradiation source. The voltage and amperage for the X-Ray source were 15 kV and 0.1 mA respectively. The signal was collected using PMT R13456 (Hamamatsu Photonics, Shizuoka, Japan Shizuoka, Japan) with a filter 721/65 Brighline HC (Semrock Inc., Rochester, NY, USA). Powder samples were prepared for measurements the same as was described in our previous work [17] For detailed analyses of the traps redistribution as an annealing temperature function, the T max -T stop (partial cleaning) experiment proposed by McKeever was performed [21]. The sample was irradiated at room temperature with the following partially heating to a temperature T stop and cooling back to room temperature (25 • C). TL curves were recorded from room temperature to 300 • C with a heating rate of 0.5 • C·s −1 and integration (detection) time of 0.1 s. Positions first maximum T max in the glow-curve versus T stop are plotted in the T stop range between 30 and 200 • C with step 10 • C to cover completely the glow curve. Figure 1 shows the XRPD patterns of the YAGG:Cr 3+ powders annealed at different temperatures. The XRPD patterns were refined by Rietveld analysis (see Figure S1), which showed the presence of pure Y 3 Al 2 Ga 3 O 12 phase of the cubic Ia3d space group [22]. The crystallographic data and refinement details of the structure including lattice parameter and grain size, are summarized in Table 1. photomultiplier tube R928P (Hamamatsu Photonics, Shizuoka, Japan) was used as a detector. The scanning range was from 250 to 680 nm for the PLE spectrum and from 460 to 820 nm for the PL spectrum with a spectral resolution of 0.2 nm. All spectra were corrected for the sensitivity of detectors and intensity excitation source. The thermoluminescence (TL) glow curves were collected with a lexygresearch-Fully Automated TL/OSL Reader (Freiberg Instruments GmbH, Freiberg, Germany) from room temperature to 300 °C with heating rates 2, 1, 0.75, 0.5, and 0.25 °C ·s −1 . Varian VF-50J/S RTG tube (Varian Medical Systems Inc., Palo Alto, CA, USA) with tungsten core and copper case as an X-ray radiation source was used as an irradiation source. The voltage and amperage for the X-Ray source were 15 kV and 0.1 mA respectively. The signal was collected using PMT R13456 (Hamamatsu Photonics, Shizuoka, Japan Shizuoka, Japan) with a filter 721/65 Brighline HC (Semrock Inc., Rochester, NY, USA). Powder samples were prepared for measurements the same as was described in our previous work [17] For detailed analyses of the traps redistribution as an annealing temperature function, the Tmax-Tstop (partial cleaning) experiment proposed by McKeever was performed [21]. The sample was irradiated at room temperature with the following partially heating to a temperature Tstop and cooling back to room temperature (25 °C ). TL curves were recorded from room temperature to 300 °C with a heating rate of 0.5 °C ·s −1 and integration (detection) time of 0.1 s. Positions first maximum Tmax in the glow-curve versus Tstop are plotted in the Tstop range between 30 and 200 °C with step 10 °C to cover completely the glow curve. Figure 1 shows the XRPD patterns of the YAGG:Cr 3+ powders annealed at different temperatures. The XRPD patterns were refined by Rietveld analysis (see Figure S1), which showed the presence of pure Y3Al2Ga3O12 phase of the cubic I ̅3d space group [22]. The crystallographic data and refinement details of the structure including lattice parameter and grain size, are summarized in Table 1.   Table 1. Cell parameter a, crystallite size D XRPD , lattice microstrain ε, an average number of Ga 3+ ions per lattice in octahedral site N(A) and tetrahedral site N(D), and fractional parameter f Ga obtained by applying the Rietveld method to the XRPD patterns.  Figure 2 presents the calculated values of grain sizes and lattice parameters of the YAGG:Cr 3+ nanopowders for the sample annealed at various temperatures. Direct dependence of the average grain size on temperature is clearly seen, increasing the temperature from 800 • C to 1300 • C led to a growth in the average crystallite size from 26(2) nm to 110(2) nm. Meanwhile, the lattice parameters decrease from 12.1806(16) Å to 12.1640(26) Å for an annealing temperature of 1100 • C, and a further rise in the temperature barely changes the lattice parameter.  Figure 2 presents the calculated values of grain sizes and lattice parameters of the YAGG:Cr 3+ nanopowders for the sample annealed at various temperatures. Direct dependence of the average grain size on temperature is clearly seen, increasing the temperature from 800 °C to 1300 °C led to a growth in the average crystallite size from 26(2) nm to 110(2) nm. Meanwhile, the lattice parameters decrease from 12.1806(16) Å to 12.1640 (26) Å for an annealing temperature of 1100 °C , and a further rise in the temperature barely changes the lattice parameter.

Microstructure
The change in the lattice parameter can be explained by the influence of the surface. The YAGG:Cr 3+ nanopowders with an average crystalline size above 50 nm do not reveal any structural alteration, while the samples smaller than 50 nm show an increase in the lattice parameter. The noticed decrease in its value is most probably related to the increase in crystallite size through the repulsive force at the surface due to unpaired electronic orbitals. These dipoles repel each other, which reduces the value of the equilibrium lattice parameter for the smaller crystallites (with a higher surface-to-volume ratio) to be greater than that of crystallites with larger sizes [23]. This is also reflected in the microstrain, which decreases with increasing crystallite size ( Figure S2). The general formula of the YAGG crystal structure can be represented as C3A2D3O12, where the C-dodecahedral site is occupied by Y 3+ ions, while A, D-octahedral, and tetrahedral sites, respectively, are occupied by Al 3+ and Ga 3+ ions [24]. Unlike Al 3+ and Ga 3+ ions, Cr 3+ can occupy only octahedral sites, because the crystal field stabilization energy of tetravalent chromium ions in tetrahedral coordination is about a third of the value in octahedral coordination [25]. Otherwise, Cr 4+ can occupy both octahedral and tetrahedral sites [26]. Accordingly, the only variable independent parameter is the occupancy of octahedral and tetrahedral sites by Al 3+ and Ga 3+ ions. The increase in annealing temperature leads to redistributions of Ga 3+ and Al 3+ ions between the different sites in the garnet lattice. Figure 3 shows the change in the occupancy of the octahedral and tetrahedral sites of the samples at different annealing temperatures. It is interesting to recall the fact that only a third of Ga 3+ is in the octahedral site, and the rest-is in the tetrahedral [23]. The change in the lattice parameter can be explained by the influence of the surface. The YAGG:Cr 3+ nanopowders with an average crystalline size above 50 nm do not reveal any structural alteration, while the samples smaller than 50 nm show an increase in the lattice parameter. The noticed decrease in its value is most probably related to the increase in crystallite size through the repulsive force at the surface due to unpaired electronic orbitals. These dipoles repel each other, which reduces the value of the equilibrium lattice parameter for the smaller crystallites (with a higher surface-to-volume ratio) to be greater than that of crystallites with larger sizes [23]. This is also reflected in the microstrain, which decreases with increasing crystallite size ( Figure S2). The general formula of the YAGG crystal structure can be represented as C 3 A 2 D 3 O 12 , where the C-dodecahedral site is occupied by Y 3+ ions, while A, D-octahedral, and tetrahedral sites, respectively, are occupied by Al 3+ and Ga 3+ ions [24]. Unlike Al 3+ and Ga 3+ ions, Cr 3+ can occupy only octahedral sites, because the crystal field stabilization energy of tetravalent chromium ions in tetrahedral coordination is about a third of the value in octahedral coordination [25]. Otherwise, Cr 4+ can occupy both octahedral and tetrahedral sites [26]. Accordingly, the only variable independent parameter is the occupancy of octahedral and tetrahedral sites by Al 3+ and Ga 3+ ions. The increase in annealing temperature leads to redistributions of Ga 3+ and Al 3+ ions between the different sites in the garnet lattice. Figure 3 shows the change in the occupancy of the octahedral and tetrahedral sites of the samples at different annealing temperatures. It is interesting to recall the fact that only a third of Ga 3+ is in the octahedral site, and the rest-is in the tetrahedral [23].
The decrease in the average grain size of the crystallites leads to a change in Ga 3+ ions distributions resulting in a decrease f Ga from 0.69(1) at crystallite size 51(2) nm to f Ga 0.63(1) at crystallite size 26(2) nm ( Figure S2) which is below the value f Ga (0.68-0.72) reported earlier for a single crystal of the same composition [27,29]. The decrease in the f Ga is probably caused by an increase in the lattice parameter of YAGG nanopowders caused by a decrease in the crystallite size. Beforehand the same results were detected on Y 3 Al 5-x Ga x O 12 single crystals where the increase in lattice parameter caused a decrease of fractional parameter f Ga . The Ga 3+ cation distributions in Y 3 Al 2 Ga 3 O 12 nanopowders are due to the binding nature of the cation-oxygen bonds and cation-cation repulsive forces. Most likely, the peculiar distribution of cations in the Y-Al-Ga system is associated with the compensation of the cation-cation repulsive force, as well as the effect of electronegativity [27].

Photoluminescence
A comparison of the PLE spectra of Cr 3+ ions in YAGG samples annealed at different temperatures from 800 • C to 1300 • C reveals the presence of a blue shift of the 4 A 2g (F) → 4 T 1g (F) transition. It can be noted that the maximum of that band shifts its position on the energy scale from 22 779 cm −1 to 23 031 cm −1 (∆E~250 cm −1 ). In contrast, the band assigned as 4 A 2g (F) → 4 T 2g (F) almost does not change its position (16 385 cm −1 ) even for the highest annealing temperature. This effect is visible in Figure 4. It should be noted that the abnormal behavior of the band 4 T 1g is observed, namely the appearance of inflexion on the shoulder from the lower energies side. This anomaly may be associated with the presence of the band 2 T 2g ( Figure S3). The position of this inflexion coincides with the corresponding line in the Sugano-Tanabe diagram ( Figure 5) [30]. single crystals where the increase in lattice parameter caused a decrease of fractional parameter fGa. The Ga 3+ cation distributions in Y3Al2Ga3O12 nanopowders are due to the binding nature of the cation-oxygen bonds and cation-cation repulsive forces. Most likely, the peculiar distribution of cations in the Y-Al-Ga system is associated with the compensation of the cation-cation repulsive force, as well as the effect of electronegativity [27].

Photoluminescence
A comparison of the PLE spectra of Cr 3+ ions in YAGG samples annealed at different temperatures from 800˚C to 1300˚C reveals the presence of a blue shift of the 4 A2g(F) → 4 T1g(F) transition. It can be noted that the maximum of that band shifts its position on the energy scale from 22 779 cm −1 to 23 031 cm −1 (ΔE ~ 250 cm −1 ). In contrast, the band assigned as 4 A2g(F) → 4 T2g(F) almost does not change its position (16 385 cm −1 ) even for the highest annealing temperature. This effect is visible in Figure 4. It should be noted that the abnormal behavior of the band 4 T1g is observed, namely the appearance of inflexion on the shoulder from the lower energies side. This anomaly may be associated with the presence of the band 2 T2g ( Figure S3). The position of this inflexion coincides with the corresponding line in the Sugano-Tanabe diagram ( Figure 5) [30]. As the Cr 3+ ion belongs to the transition metal ions, its spectroscopic properties depend much more on the crystal field strength than is the case for, e.g., lanthanide ions. For example, in the presence of a low field, the Cr 3+ luminescence occurs from the spin-allowed 4 T2g → 4 A2 transition (broadband emission with a short lifetime), but for a high crystal field (more than 2.1), the dominant luminescence originates from the spin-forbidden 2 E→ 4 A2 transition, which results in the presence of sharp zero phonon R lines, a phonon sideband, and a longer decay time [30,31]. In the YAGG host, the Cr 3+ ion substitutes the Al 3+ site with the octahedral symmetry, so it is possible to determine the values of crystal field parameters by using a Tanabe-Sugano diagram for a d 3 system [30]. The Racah parameter B, as well as the ligand field splitting term Dq for each annealing temperature, B as the point of intersection of the vertical line representing 20Dq/B, with the term line of the lowest 4 T2g(F) state on the Tanabe-Sugano diagram. Finally, using the calculated Racah parameter B, one can determine the Dq value representing the crystal field strength for this system as well as the β = B/B0 (where B0 is the Racah parameter for free Cr 3+ ion, equal to 1030 cm −1 ). All the calculated parameters are presented in Table 2. The slightly decreasing distance between 4 T1g(F) and 4 T2g(F) terms over the range of temperatures investigated indicates a decreasing repulsion interaction of the d electrons and, hence, an expansion of the d electrons cloud. This effect is called the nephelauxetic effect [33]. In addition, with the increase of annealing temperature (and therefore with the crystallite size) an increase of the β parameter, determining the degree of bonding covalence is observed. In the case of the investigated YAGG:1%Cr 3+ sample, the bonding covalence degree appears to decrease with the crystallite size. As can be seen from the data obtained, the YAGG:Cr 3+ samples annealed at lower temperatures (between 800 to 1000˚C) seem to be identical in terms of crystal field calculations. Thereafter, as the annealing temperature increases, the Dq/B parameter starts to decrease and reaches a minimum (~24) at 1200 °C . However, despite the observed tendency for higher temperatures to decrease the crystal field intensity with crystallite size, a breakdown is observed at 1300 °C . At this temperature, the redistribution of ions does not change compared to the sample annealed at 1100 °C . This tendency is similar to the data for the lattice parameter and Ga 3+ and Al 3+ sites occupancy. As the Cr 3+ ion belongs to the transition metal ions, its spectroscopic properties depend much more on the crystal field strength than is the case for, e.g., lanthanide ions. For example, in the presence of a low field, the Cr 3+ luminescence occurs from the spinallowed 4 T 2g → 4 A 2 transition (broadband emission with a short lifetime), but for a high crystal field (more than 2.1), the dominant luminescence originates from the spin-forbidden 2 E→ 4 A 2 transition, which results in the presence of sharp zero phonon R lines, a phonon sideband, and a longer decay time [30,31]. In the YAGG host, the Cr 3+ ion substitutes the Al 3+ site with the octahedral symmetry, so it is possible to determine the values of crystal field parameters by using a Tanabe-Sugano diagram for a d 3 system [30]. The Racah parameter B, as well as the ligand field splitting term Dq for each annealing temperature, were found by determining the positions of the two excitation peaks evident in Figure 4, calculating their energy ratio, and locating these ratios on the proper Tanabe-Sugano diagram [32]. The result of this procedure is presented in Figure 5. The calculated ratios increase with the temperature from 1.378 to 1.417 and obtained 10Dq/B parameters decrease from 27.203 to 23.730, respectively. Hence, we can determine the values of the parameter B as the point of intersection of the vertical line representing 20 Dq/B, with the term line of the lowest 4 T 2g (F) state on the Tanabe-Sugano diagram. Finally, using the calculated Racah parameter B, one can determine the Dq value representing the crystal field strength for this system as well as the β = B/B 0 (where B 0 is the Racah parameter for free Cr 3+ ion, equal to 1030 cm −1 ). All the calculated parameters are presented in Table 2.
The slightly decreasing distance between 4 T 1g (F) and 4 T 2g (F) terms over the range of temperatures investigated indicates a decreasing repulsion interaction of the d electrons and, hence, an expansion of the d electrons cloud. This effect is called the nephelauxetic effect [33]. In addition, with the increase of annealing temperature (and therefore with the crystallite size) an increase of the β parameter, determining the degree of bonding covalence is observed. In the case of the investigated YAGG:1%Cr 3+ sample, the bonding covalence degree appears to decrease with the crystallite size. As can be seen from the data obtained, the YAGG:Cr 3+ samples annealed at lower temperatures (between 800 to 1000 • C) seem to be identical in terms of crystal field calculations. Thereafter, as the annealing temperature increases, the Dq/B parameter starts to decrease and reaches a minimum (~24) at 1200 • C. However, despite the observed tendency for higher temperatures to decrease the crystal field intensity with crystallite size, a breakdown is observed at 1300 • C. At this temperature, the redistribution of ions does not change compared to the sample annealed at 1100 • C. This tendency is similar to the data for the lattice parameter and Ga 3+ and Al 3+ sites occupancy. The PL spectra of samples annealed at temperatures from 800 to 1300 • C are shown in Figure 6. The sharp and strong PL peak at ∼690 nm, is related to the 4 A 2g → 2 E g transition, while the broadband is related to the 4 T 2g → 4 A 2g transition.  The PL spectra of samples annealed at temperatures from 800 to 1300˚C are shown in Figure 6. The sharp and strong PL peak at ∼690 nm, is related to the 4 A2g → 2 Eg transition, while the broadband is related to the 4 T2g → 4 A2g transition. It was reported elsewhere, that the PL intensity of the Cr-doped garnet may strongly depend on the particle size [34]. In this work, particularly for samples annealed at temperatures from 800 to 1000˚C, the PL intensity has almost the same intensity. This is consistent with the reported structural features-for these samples, the average particle size is found to be almost the same. However, for lower annealing temperatures a significant number of O-H groups remain on the particle surfaces or in the pores and it can lead to luminescence quenching [35]. With a further increase in annealing temperature, an increase in intensity is also observed, which reaches its maximum value for a temperature of 1200˚C and then remains unchanged. It was reported elsewhere, that the PL intensity of the Cr-doped garnet may strongly depend on the particle size [34]. In this work, particularly for samples annealed at temperatures from 800 to 1000 • C, the PL intensity has almost the same intensity. This is consistent with the reported structural features-for these samples, the average particle size is found to be almost the same. However, for lower annealing temperatures a significant number of O-H groups remain on the particle surfaces or in the pores and it can lead to luminescence quenching [35]. With a further increase in annealing temperature, an increase in intensity is also observed, which reaches its maximum value for a temperature of 1200 • C and then remains unchanged.

Thermoluminescence Analysis
To determine the effect of structural changes on the traps formation and redistribution, the TL curves for all investigated powders after irradiation by X-ray were recorded and analyzed. The first and dominant TL peak for the YAGG:Cr 3+ sample is observed at around 60 • C (Figure 7). Furthermore, a second high-temperature peak with a maximum at 190 • C is more pronounced at lower annealing temperatures. In YAGG:Cr 3+ annealed at 900 • C, the two TL peaks reflect two well-defined series of traps. As the annealing temperature increases, the intensity of the second peak decreases slightly and it becomes less prominent compared to the first peak, whose intensity increases. Importantly, both peaks have a similar symmetrical shape, suggesting that they may be the result of a superposition of a series of traps with a continuous energies distribution [21,36]. To determine the effect of structural changes on the traps formation and redistribution, the TL curves for all investigated powders after irradiation by X-Ray were recorded and analyzed. The first and dominant TL peak for the YAGG:Cr 3+ sample is observed at around 60 °C (Figure 7). Furthermore, a second high-temperature peak with a maximum at 190˚C is more pronounced at lower annealing temperatures. In YAGG:Cr 3+ annealed at 900˚C, the two TL peaks reflect two well-defined series of traps. As the annealing temperature increases, the intensity of the second peak decreases slightly and it becomes less prominent compared to the first peak, whose intensity increases. Importantly, both peaks have a similar symmetrical shape, suggesting that they may be the result of a superposition of a series of traps with a continuous energies distribution [21,36]. As can be seen from the results of structural studies carried out for the samples doped with chromium, three critical temperatures can be distinguished for the powders studied, namely 900, 1100, and 1300˚C. At 900˚C, crystal structure formation was observed for the garnet synthesis by the Pechini method [17]. The temperature of 1100˚C was chosen based on the minimum values of the lattice parameter and the particle size, which is still less than 100 nm. The third is 1300˚C, at which the lattice parameter begins to increase and the crystal field decreases. To further analyze the traps contributing to the main thermoluminescence peaks, the Tmax-Tstop method was carried out for selected annealing temperatures (Figure 8 left panel). In addition, the Initial Rise method [37] was used to determine the energy from each of the recorded curves. Using data obtained, plots of the dependence of Tmax (black square) and activation energy (blue square) on Tstop value were drawn for observed traps, which are presented in Figure 8   As can be seen from the results of structural studies carried out for the samples doped with chromium, three critical temperatures can be distinguished for the powders studied, namely 900, 1100, and 1300 • C. At 900 • C, crystal structure formation was observed for the garnet synthesis by the Pechini method [17]. The temperature of 1100 • C was chosen based on the minimum values of the lattice parameter and the particle size, which is still less than 100 nm. The third is 1300 • C, at which the lattice parameter begins to increase and the crystal field decreases. To further analyze the traps contributing to the main thermoluminescence peaks, the T max -T stop method was carried out for selected annealing temperatures (Figure 8 left panel). In addition, the Initial Rise method [37] was used to determine the energy from each of the recorded curves. Using data obtained, plots of the dependence of T max (black square) and activation energy (blue square) on T stop value were drawn for observed traps, which are presented in Figure 8 (right panel). Figure 8. TL glow curves were detected with the T max -T stop methods and their analysis using the Initial-Rise method (blue points in the right row of panels). Samples were charged with X-rays for 5 min, β-0.5 • C/s. Two maxima are clearly evident in the plots, which are of different natures. The first maximum is linear with a slope near unity, indicating a series of first-order peaks with a quasi-continuous distribution of peaks (and, therefore, of trapping centers) [38,39]. The second maximum consists of a single first-order peak only in the T max -T stop part of the curve (150-200 • C) and in the further course is simply a line with zero slope [38]. This is because the peak has not shifted as the initial population of trapped charges decreases. From the point of view of the activation energy, the first maximum in all samples is the same and is about 0.75 ± 0.02 eV, which is close to the value observed previously for the same matrix with different co-dopants [17,40]. In contrast, the activation energy of the second maximum noticeably decreased from about 0.9 to 0.5 eV with increasing an annealing temperature. The invariability of the position of the maximum with decreasing activation energy can be explained by the following Equation (1): where T m is the glow curve maximum, E is the activation energy, β is the heating rate (in K/s), and s-frequency factor (s −1 ). Equation (1) shows that the frequency factor also plays an important role in the de-trapping process. As the activation energy of the second maximum decreases from 0.9 to 0.5 eV, the value of the frequency factor decreases from 10 8 to 10 3 s −1 , and the process of releasing trapped electrons occurs more slowly [37,41]. Finally, it is likely that one TL peak with a position at a higher T m may have a lower activation energy than the previous one. Combining these results with the previous analysis of the structure and optical properties, it can be concluded with a high probability that the traps with lower energy values are related to changes occurring inside the phosphors. In particular, morphology, phase change, redox reactions of the dopant ions, changes due to clustering of such dopants, etc. Specifically, one of the limiting points may be -OH groups, which may be present in samples after lower annealing temperatures [35] and which can transform into oxygen vacancies as a result of annealing at higher temperatures.

Conclusions
It was found, that increasing the annealing temperature to 1100 • C leads to a decrease in the lattice parameter to 12.164, after which it remains almost unchanged. In parallel, a redistribution of the Ga 3+ and Al 3+ ions between octa-and tetrahedral sites in the garnet lattice occurs. Above 1100 • C, most Ga 3+ ions (up to 70%) remain in the tetrahedral site while Al ions (up to 55%) move to the octahedral site. These structural changes correlate with the optical characteristics of both PL and PersL. As the grain size increases, the electronphonon coupling decreases, whereas the crystal-field strength increases. A similar trend is observed for thermoluminescence curves. The maximum of the TL intensity reached 1100 • C and remains unchanged for higher temperatures.
It can therefore be concluded that the higher annealing temperature (>1100 • C) did not improve the optical properties of studied phosphors. Consequently, the YAGG phosphor annealed at 1100 • C, showing an acceptable degree of particle agglomeration, may already be suitable for practical applications as starting materials for the production of, among others, high-quality optical ceramics and luminescent markers for imaging in the first biological window.